Under what conditions is the matrix product defined?
Not possible.
Practice makes perfect
We want to calculate the matrix product, if possible. To do so, we need to recall that the multiplication of two matrices is defined only if the number of columns of the first matrix is equal to the number of rows of the second matrix.
Let's consider the given matrices.
2 & 11
0 & -3
-6 & 7
& and 0& 8& -5 12 & 0 & 9 4 & -6 & 7
3* 2 & 3* 3
The dimensions of the first matrix are 3* 2. This means it has three rows and two columns. The dimensions of the second matrix are 3 * 3, so it has three rows and three columns. Since 2 ≠3, the number of columns of the first matrix is not equal to the number of rows of the second one. Therefore, the multiplication of the matrices is not possible.
